package path;

/**
 * 二、路径问题
 * 5. 最小路径和
 * 2024-10-19
 */
public class demo9 {
    public int minPathSum(int[][] grid) {
        //1. 创建 dp 表
        int m = grid.length;
        int n = grid[0].length;
        int[][] dp = new int[m+1][n+1];

        //2. 初始化
        for (int i = 0; i <= n; i++) {
            dp[0][i] = Integer.MAX_VALUE;
        }
        for (int i = 0; i <= m; i++) {
            dp[i][0] = Integer.MAX_VALUE;
        }
        dp[0][1] = dp[1][0] = 0;

        //3. 填表
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                dp[i][j] = Math.max(dp[i-1][j], dp[i][j-1]) + grid[i-1][j-1];
            }
        }
        return dp[m][n];
    }
}
